Lightmap Pack is non-uniformly scaling my geometry?
The purpose of Lightmap Pack command is to utilize as much UV space as possible by storing each face (individually) in the UV space bounds.

I must admit that I can't tell you how exactly the algorithm works, but if you consider two similar objects that differ only from the lenght of a face (8.0 vs 8.1) you'll see different results of the lightmap pack command.

In the shortest parallelogram, each face is not "enough" different from the average face size of the object, so they are all stored with the same size in the UV. The proportion are not preserved. They are stretched to fill the boundaries.



In longest parallelogram, Blender sees instead that some faces are much longer than other (they just get over the alghorithm thereshold), so it is aware that they should need more space.

Notice that also in this case, despite what could it seem, proportions are not mantained. The Face is 2:8.1, while the UV is more 2:4. That's because Blender look for the best way to fill all the UV space, regardless proportion. This is a uv layout for Baking textures efficently.



If you are interested in keeping the proportions, Lightmap pack is not the right UV unwrapping method.

In the brought example I would separate each face by extruding them individually by a 0 factor, than Crtl+i to invert seelction and Canc to delete unwanted faces.

 

Than a simple Unwrap or Smart unwrap, should pack all the faces preserving their proportions in the UV map.